Theoretical and experimental study of the effective linear and nonlinear optical response of nano-structured silicon

We study the effective optical linear and the effective optical third-order nonlinear response of some Si based nano-structures. Particularly, the optical response of nano-porous silicon layers on crystalline silicon substrate, in function of fill fraction and light wavelength is investigated. Starting from Bruggeman's effective medium theory and Sellmeier's dispersion formalism (for silicon), we derive simplified formulae that describe the dependences of effective optical linear and third-order nonlinear response on both fill fraction and wavelength, in the spectral range covering visible and near-infrared. They are in agreement with the experimental data obtained from reflectivity measurement (in the case of effective linear refractive index) and by reflection intensity scan (in the case of effective third-order nonlinearity). Furthermore, the electronic and thermal nonlinear optical response of periodically nano-patterned and un-patterned silicon-on-insulator (SOI) is also studied using a reflection Z-scan setup with a high-repetition-rate femto-laser (at 800 nm wavelength) and a new procedure for discrimination between electronic and thermal nonlinearities. The electronic nonlinear response of nano-structured SOI is strongly enhanced in comparison with those of un-patterned SOI.